Here's a very brief introduction of who they are...

The Paternoster Gang are made up of 3 people. Vastra the Silurian, Strax the Sontaran and Jenny Flint who is human. These 3 are detectives in Victorian London and are named after Paternoster Row in London. Vastra, along with fellow Silurians, had awoken during the construction of part of the London Underground and had wanted to take revenge on innocent tunnel workers for the deaths of her sisters. Eventually Vastra hired Jenny. There relationship has now become romantic.

Paternoster Gang in Doctor Who!

Vastra and Jenny were part of the Doctor's Army on Demon's Run in Series 6 (A Good Man Goes to War). Commander Strax was originally a nurse. He as well owed the Doctor a debt. Strax helped out the Doctor in his battle on his Demon's Run. Strax was killed in this battle with the Headless Monks. This wasn't the end of Strax! 2 days after the battle Jenny and Vastra returned to Demon's Run to retrieve and revive Strax. They woke Strax up, informing him that he had not died since they had used alien technology to heal his wounds. Jenny said that he had never truly passed away thanks to the resurrection technology and he had been in a state of unconsciousness for two days while the resurrection device healed him. Jenny and Vastra had offered to take Strax back to London with them. At first Strax refused the offer. He suddenly changed his mind and went to London in 1888. Strax is now Vastra's butler.

Is A Spin Off Likely To Happen?

Steven Moffat (Head Writer of Doctor Who) has said that he is 'hesitant to bring back the Paternoster Gang to Doctor Who for another appearance. The Paternoster Gang were last seen in the Series 8 opener (Deep Breath) helping out the newly regenerated Doctor (Peter Capaldi) and Clara Oswald (Jenna Coleman). The gang were of course happy to help.

Moffat explained in the DWM...

“I’m always slightly worried that you can’t keep repeating the joke. And there’s always talk of the spin-off, and the Beeb would do it in a heartbeat… but… I dunno. The moment you start relying on something, you should probably throw it away. I always kind of feel that nothing should stay in the Doctor’s life. You can have River for a few years, but then River has to go.” - Steven Moffat

We have not seen the Paternoster Gang since Series 8. Fingers crossed we see them again very soon. There has been NO confirmation whether or not they are going to be Series 9. Fingers crossed they get there own Spin-Off show. The Doctor Who Spin-Off Shows have been extremely successful, like 'The Sarah Jane Adventures' and 'Torchwood'. This Spin-Off is likely to be just as successful. The Doctor could even make an appearance in this show. The Spin-Off show I think would actually see the characters personalities evolve a bit more. #

Strax, Clara and Vastra in Deep Breath

It would be great to see them again after all this time!

Above is a video showing the Paternoster Gang in Doctor Who 'The Crimson Horror'.